With many conservatives now insisting they won't vote for any government spending bill that doesn't block the president's executive action on immigration, could House Minority Leader Nancy Pelosi's Democrats get a sweeter deal in exchange for votes to pass a bill to fund the government beyond Dec. 11?

Conservatives spent much of Wednesday firing up their base, building opposition to any spending bill — omnibus, continuing resolution or "cromnibus" — that doesn't explicitly defund the immigration order.

"Some will say we'll vote to fund it for now and then we'll have reinforcements from the Senate next year," Rep. Steve King, R-Iowa, said during a press conference-turned-tea-party-rally Wednesday. "Two problems with that: One of them is that we would have lost our virtue. How do we make the argument that we're going to defend the Constitution in January, February, March or April, if we're not willing to defend the Constitution in December?"

King said he was unwilling to vote for any bill that funds the Department of Homeland Security without blocking the executive action, even if it only funded the department for a month.

"This is a matter of principle," King said. "This is a matter of constitutional issue." But if Republicans can't pass a spending bill on their own, won't that force Republicans to seek Democratic votes and potentially move the legislation further to the left? "If they do, they do," King said. "It's better than damaging the virtue of Republicans."

That seemed to be the position of many Republicans in attendance at Wednesday's outdoor press conference, which included Sen. Ted Cruz of Texas, King, Michele Bachmann of Minnesota, Louie Gohmert of Texas, Randy Weber of Texas, Tim Huelskamp of Kansas, and other conservative voices.

"There's an old saying: It's never wrong to do the right thing," Weber told CQ Roll Call before the press conference started. "And so if we vote for what the American people want, if the Democrats want to vote for something the American people don't want and be held accountable in their own districts, that's up to them."

"Funding unconstitutional actions for any length of time is a real problem," Gohmert said.

That position puts GOP leadership in a tough bind.

"The same members who oppose an omni/CR because it would 'fund amnesty' would oppose a short-term CR for the very same reason," a senior GOP aide told CQ Roll Call in an email. "It's a transparent attempt to provoke a shutdown simply to ingratiate themselves in the eyes of some Washington-based activists."

Republicans want to avoid a shutdown, but a steadfast refusal from conservatives to vote for anything that may fund the immigration executive action leaves them in need of votes. And if Obama won't sign a bill that blocks his action, and if conservatives won't vote for a bill that funds it, Republicans will have to rely on Democrats to pass a spending bill — and that could put Democrats in a strong negotiating position.

Whether Democrats could get a full omnibus spending bill that funds every department until October remains to be seen. Senate Majority Leader Harry Reid, D-Nev., has already shown some support for the current cromnibus plan, and Minority Whip Steny H. Hoyer, D-Md., gave the plan — which would fund everything for the remainder of the fiscal year with the exception of Homeland Security, which would be funded until March — said he wasn't a "hard 'no' or 'yes.'"

The White House, though, doesn't like the idea — though there has been no promise of a presidential veto if such a bill makes it to President Barack Obama's desk.